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The Berry–Esseen bound in de Jong’s CLT

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  • Döbler, Christian

Abstract

We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate U-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).

Suggested Citation

  • Döbler, Christian, 2024. "The Berry–Esseen bound in de Jong’s CLT," Statistics & Probability Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s016771522400213x
    DOI: 10.1016/j.spl.2024.110244
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    References listed on IDEAS

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    1. Vitale, Richard A., 1992. "Covariances of symmetric statistics," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 14-26, April.
    2. de Jong, Peter, 1990. "A central limit theorem for generalized multilinear forms," Journal of Multivariate Analysis, Elsevier, vol. 34(2), pages 275-289, August.
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